Reward inequity can promote both public goods production and free riding

When animals in groups cooperate, individuals sometimes produce a 'public' good that benefits many or all group members and receive a private reward (that is not shared with others). The rate at which rewards are given and how rewards are distributed among contributors is likely to affect the occurrence of public goods production, but empirical evidence is contradictory. Here, we develop a game-theoretic model to investigate how reward rate and distribution affect the production of a public good. Our model is applicable to various scenarios in which individuals can be rewarded for public goods contributions; for example, sentinel behaviour, intergroup contest participation and collective hunting. The model predicts that inequitable distribution of rewards results in higher public goods contributions by some individuals but free riding by others because it induces competition among potential contributors. We also find that a high reward rate promotes public goods contributions but only up to a point, after which further rewards suppress contributions. This suggests that social factors such as inequity and competition might interact to affect the outcome of common public goods scenarios.